Rabbi Yeshayahu Hollander, a member of the Sanhedrin said,
“The Jews are commanded to be a nation of priests,” Rabbi Hollander [told Breaking Israel News,] citing a verse in Exodus.
But you shall be to Me a kingdom of priests and a holy nation.’ These are the words that you shall speak to the children of Yisrael.” Exodus 19:6
Clearly, the Torah is stating that Yisrael is to be "a kingdom of priests and a holy nation."
Electing a king is qualified by the statement in the passuk, "one whom the L-rd, your G-d, chooses;" which is further qualified by the passage in 2 Samuel 6.21 [And David said unto Michal: 'Before the L-RD, who chose me above thy father, and above all his house, to appoint me prince over the people of the L-RD, over Israel, before the L-RD will I make merry.] and also qualified by ["Howbeit the L-RD, the G-D of Israel, chose me out of all the house of my father to be king over Israel for ever; for He hath chosen Judah to be prince, and in the house of Judah, the house of my father, and among the sons of my father He took pleasure in me to make me king over all Israel;"] OBVIOUSLY, HaShem chose David to be King over all Yisrael, the prophesied "kingdom of priests and a holy nation!"